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16.360 Lecture 14

16.360 Lecture 14. Today. Orthogonal coordinate systems. The Cartesian (rectangular) coordinate system The cylindrical coordinate system The spherical coordinate system. 16.360 Lecture 14. Cartesian coordinate system. z. dl. . . y. x. 16.360 Lecture 14.

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16.360 Lecture 14

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  1. 16.360 Lecture 14 • Today Orthogonal coordinate systems • The Cartesian (rectangular) coordinate system • The cylindrical coordinate system • The spherical coordinate system

  2. 16.360 Lecture 14 • Cartesian coordinate system z dl   y x

  3. 16.360 Lecture 14 • Cartesian coordinate system z directions of area y x

  4. z y x 16.360 Lecture 14 • Cylindrical coordinate system

  5. z y x 16.360 Lecture 14 • the differential areas and volume

  6. 16.360 Lecture 14 Example: cylindrical area z 5 3 60 y 30 x

  7. 16.360 Lecture 14 • Spherical coordinate system

  8. 16.360 Lecture 14 • differential volume in Spherical coordinate system

  9. 16.360 Lecture 14 • Examples (1) Find the area of the strip (2) A sphere of radius 2cm contains a volume charge density Find the total charge contained in the sphere

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